Then, the labeling could be modified: the first time the PTAH inequality appears it could be labeled (P);
then the maximum-entropy inequality could be labeled (G), followed by Hölder’s inequality (already labeled (H));
and the statement could be “the inequalities (A) through (G) are equivalent, each is a special case of (H),
and (H) is a special case of (P). However, it appears that none of the reverse implications hold.”